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On the Optimality and Interconnection of VLB Networks

On the Optimality and Interconnection of VLB Networks. Moshe Babaioff and John Chuang UC Berkeley IEEE INFOCOM 2007 Anchorage, Alaska, USA May 8, 2007. Main Points. Universal optimality of Valiant Load Balancing (VLB) network under node failures (in paper)

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On the Optimality and Interconnection of VLB Networks

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  1. On the Optimality and Interconnection of VLB Networks Moshe Babaioff and John Chuang UC Berkeley IEEE INFOCOM 2007 Anchorage, Alaska, USA May 8, 2007

  2. Main Points • Universal optimality of Valiant Load Balancing (VLB) network under node failures (in paper) • Interconnection of multiple VLB networks • Interconnection challenges • Generalization: m-hubs VLB • Support peering and transit relationships Babaioff & Chuang 2007

  3. Backbone Network Design r 1 2 r • Many challenges: • Traffic matrix can change over short and long timescales • Customers expect high availability and low congestion • Network operator must design for low congestion and high fault tolerance over the lifetime of the network r r n 3 Network? r 4 … r Babaioff & Chuang 2007

  4. Valiant Load-Balancing (VLB)[Zhang-Shen & McKeown; Kodialam et. al.] • Clean-slate approach to backbone design: • Design a network that supports any legal traffic matrix (fij)i,j • Input: • n : the number of nodes • r : bound on each node’s ingress and egress rates (hose model) • Output: A network that supports any legal traffic matrix on the n nodes: • Capacity cij on each edge (i,j) • A routing scheme that respects the edge capacities Babaioff & Chuang 2007

  5. Valiant Load-Balancing (VLB)[Zhang-Shen & McKeown] 1 2 • fij : rate from i to j • Σj fij ≤r , Σi fij ≤r • Two-stage routing of fij : • i sends fij/n to each node k • k forwards to j • For any legal traffic matrix, flow of at most: Σj fij/n ≤r/n per stage per edge • Total capacity: 2r(n-1) is optimal • Additional results for heterogeneous nodes, fault tolerance 2r/n n 3 r 1 … 4 r r Babaioff & Chuang 2007

  6. ? ? ? VLB Interconnection 1 2 • How should multiple VLB networks interconnect with one another? • How to generalize the load-balancing routing algorithm • How to support different interconnection relationships, e.g., transit and peering • Are the efficiency and robustness properties of a single VLB network retained? 6 3 5 4 B C A E D Babaioff & Chuang 2007

  7. VLB Generalization: m-hubs VLB • Each stream is equally load-balanced on m nodes(the hubs) • n-hubs = VLB • 1-hub = star • Fact: any m-hubs network can support any legal traffic matrix, and it has optimal network capacity of 2r(n-1). Capacity: 2(n-m)m (r/m) + m(m-1) (2r/m) = 2r(n-1) r/m r/m r/m 2r/m Babaioff & Chuang 2007

  8. Peering of Two Networks 1 2 • Two networks connect at a set of mshared locations • Network x has nx nodes, each with homogeneous rate of rx (possibly n1≠n2 and r1≠r2) • There is a bound of Rp on the total interconnection rate to/from a network 6 3 5 4 B C A E D Babaioff & Chuang 2007

  9. “Two m-hubs VLB Peering Network” 1 2 • Two m-hubsVLB networks peering at the hubs • 3-stage routing scheme: • traffic load balanced on the mhubs • traffic sent across peering edges • traffic delivered to destination • Each network x has optimal capacity: 2rx(nx -1) • Capacity of Rp/m on each of the 2m directed peering edges • Total interconnection capacity of 2Rp(optimal) 6 3 5 4 B C A E D Babaioff & Chuang 2007

  10. Peering of 2 Networks: Results Theorem: The “two m-hubs VLB peering network” can support any legal traffic matrix and has minimal capacity in each network and minimal interconnection capacity. • Result extends to q>2 networks in the case of universally shared locations: all networks share m>0 locations • Extension to node failures Babaioff & Chuang 2007

  11. Interconnection without Universally Shared Locations • With three or more VLB networks, it may be infeasible to require a set of interconnection points universally shared by all networks • Networks have different coverage areas • Raises entry barrier for new networks; reduces evolvability • Consider alternate VLB interconnection schemes • Transit vs. peering schemes • Note: routing stages will have to increase Babaioff & Chuang 2007

  12. q: # of networks : hubs : data : destination VLB Bilateral Peering x1 • Traffic load-balanced on local hubs • Traffic forwarded to peering nodes for destination network • Traffic sent across peering edges • Traffic load-balanced on destination network’s hubs • Traffic delivered to destination node x2 x3 xq • Traffic load-balanced on local hubs • Traffic forwarded to peering nodes for destination network • Traffic sent across peering edges • Traffic load-balanced on destination network’s hubs • Traffic delivered to destination node Babaioff & Chuang 2007

  13. q: # of networks : hubs : data : destination VLB Bilateral Peering x1 Rp • Capacity for each networkx: Cx=2rx(nx-1)+2Rp(q-2)(within constant factor of optimal) • Interconnection capacity: Rp (q-1)q(optimal for peering) Rp Rp Rp x2 x3 xq Rp Babaioff & Chuang 2007

  14. q: # of networks : hubs : data : destination VLB Transit (“VLB over VLBs”) z (transit) • Traffic load-balanced on local hubs • Traffic forwarded to transit network Z • Traffic load-balanced on transit hubs • Traffic forwarded to peering nodes • Traffic forwarded to destination network (destination hubs) • Traffic delivered to destination node x1 x2 xq-1 • Traffic load-balanced on local hubs • Traffic forwarded to transit network Z • Traffic load-balanced on transit hubs • Traffic forwarded to peering nodes • Traffic forwarded to destination network (destination hubs) • Traffic delivered to destination node Babaioff & Chuang 2007

  15. q: # of networks : hubs : data : destination VLB Transit (“VLB over VLBs”) z(transit) • Capacity of stub network x: 2rx(nx -1) • Capacity of transit network z: 2rz(nz-1)+2Rp(q-2) • Interconnection capacity: 2Rp (q-1) Theorem: Any interconnection network by a transit network must have at least these capacities in each network and at least as much interconnection capacity. • Proves the optimality of VLB as the transit scheme. Rp Rp Rp Rp Rp x1 x2 xq-1 Babaioff & Chuang 2007

  16. VLB Peering vs. Transit S= Σy 2ry(ny -1)  Transit scheme more scalable in number of networks (q) Babaioff & Chuang 2007

  17. Summary • Established universal optimality of VLB under node failures (not presented today) • Generalized m-hubs VLB network serves as building block for VLB interconnection • m-hubs VLB design retains desirable properties of VLB while allowing diverse VLB networks to interconnect • Can support both peering and transit relationships • Established optimality for VLB transit, and within constant factor of optimality for VLB peering • Open questions: • Support simultaneous transit and peering • Fault tolerance: failure of nodes, edges, transit networks • Strategic interaction between VLB networks Babaioff & Chuang 2007

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